Abstract
Neutrosophic set (NS) is an extensively used framework whenever the imprecision and uncertainty of an event is described based on three possible aspects. The association, neutral, and nonassociation degrees are the three unique aspects of an NS. More importantly, these degrees are independent which is a great plus point. On the contrary, neutrosophic graphs (NGs) and single-valued NGs (SVNGs) are applicable to deal with events that contain bulks of information. However, the concept of degrees in NGs is a handful tool for solving the problems of decision-making (DM), pattern recognition, social network, and communication network. This manuscript develops various forms of edge irregular SVNG (EISVNG), highly edge irregular SVNG (HEISVNG), strongly (EISVNG), strongly (ETISVNG), and edge irregularity on a cycle and a path in SVNGs. All these novel notions are supported by definitions, theorems, mathematical proofs, and illustrative examples. Moreover, two types of DM problems are modelled using the proposed framework. Furthermore, the computational processes are used to confirm the validity of the proposed graphs. Furthermore, the results approve that the decision-making problems can be addressed by the edge irregular neutrosophic graphical structures. In addition, the comparison between proposed and the existing methodologies is carried out.
Highlights
PreliminariesSome basic definitions related to our graphical work such as intuitionistic FGs (IFGs), singlevalued NGs (SVNGs), and degree of SVN graph (SVNG) are presented
Neutrosophic set (NS) is an extensively used framework whenever the imprecision and uncertainty of an event is described based on three possible aspects. e association, neutral, and nonassociation degrees are the three unique aspects of an NS
We propose the definitions of edge irregular and highly edge irregular singlevalued NGs (SVNGs)
Summary
Some basic definitions related to our graphical work such as IFG, SVNG, and degree of SVNG are presented . Let G (V , E) be an IFG, where V is the collection of vertices and Eis the collection of edges. Let G (V , E) be a SVNG, where V is the collection of vertices and Eis the collection of edges. By Definition 4, we find the degrees of its vertices of Figure 3 which is given below. E SVN-weighted aggregation (SVNWA) operator is denoted and defined by Ni v~3 v1. (0.2, 0.6, 0.8) Figure 2: Single-valued neutrosophic graph. 0.6, 0.5) (0.4, v~1 (0.4, 0.5, 0.2) Figure 3: Degrees of single-valued neutrosophic graph. E SVN-weighted geometric (SVNWG) operator is denoted and defined by. E score function in a SVNS is denoted and defined by S(Ni) (T +1 − I +1 − F_)/3 , where (T, I, F_) represents the_membership, ind⌢eterminacy, and nonme⌢mbership grades, respectively Definition 8 (see [27]). e score function in a SVNS is denoted and defined by S(Ni) (T +1 − I +1 − F_)/3 , where (T, I, F_) represents the_membership, ind⌢eterminacy, and nonme⌢mbership grades, respectively
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